The ambiguity function is used to examine different waveforms or signals which include unknown signals, extraneous noise, and various reflections, and to extract signal or target information wherein the information signals have a certain degree of accuracy and reliability. The cross-ambiguity function (CAF) is typically used to locate some type of “signal” which has certain unknown parameters, and various types of parameterization can be employed and match a model to processed data.
A common use of the CAF is in relation to sonar and radar applications to locate signals having unknown time delay and frequency offset (Doppler shift). The ambiguity functions can be used to estimate the range and velocity of “targets” and, more generally, of the cross-ambiguity function to estimate target distribution functions.
For example, radar operations provide a two-dimensional function of radar range and Doppler frequency determined by the transmitted waveform. The reception of the radar signals includes not only the reflected transmitted waveform but also associated noise and other signals. The principles of radar processing are well-established as described in Nathanson, F. E., 1991: Radar Design Principles, 2d ed., McGraw-Hill, 360-369; and Skolnik, M. I., 1980: Introduction to Radar Systems, 2d ed., McGraw-Hill, 411-420.
For example, if a signal, s(t), is transmitted and returns with additive noise, r(t), the time delay (T) corresponds to range and the Doppler shift corresponds to target velocity. A three-dimensional CAF surface is generated as a grid of points and characterized by time, frequency and amplitude. Provided that the Doppler effect can be approximated by a frequency shift, the presence of a target is indicated by a prominent peak in the CAF surface. Determining the actual CAF peak generally requires certain interpolation techniques.
The CAF procedure also applies to signals in domains other than time delay and frequency offset. For example, CAF processing is used in communications, optics, imaging, audio and medical applications.
In communications applications, wired or wireless networks are employed for communication between various devices, such as cell phones and computers. Typically, digitally modulated signals are transmitted between nodes of a network.
One example is satellite communications networks where terminals transmit through satellite transponders, terrestrial systems where terminals transmit through repeating towers, and indoor local area networks where terminals transmit through central repeating elements. Locating the source of an unknown signal involving satellite communications is described in U.S. Pat. No. 6,018,312 wherein the receiver coherently processes received signals including reference signals. CAF processing of the reference and unknown signals determine the relative differential time offset (DTO) and differential frequency offset (DFO) which is used to calculate the position of the unknown source.
Another example relates to the computer elements connected to networks that provide a variety of user services. Examples include telephone traffic with digital voice encoding, video conferencing, wide area computer network connectivity, and internet service. In such applications, it is desirable to maximize the network traffic capacity in a given bandwidth in the presence of interference and noise.
Various schemes are used to enhance efficiency and transfer more traffic within a designated bandwidth, however there are inherent inefficiencies due to sufficient signal to noise ratio or coding redundancy. More communicators could use an allocated bandwidth provided there were some means for detecting the excess signal margin, as well as a means for demodulating signals in the presence of interference. In general, despite advancements in transmission and reception, conventional systems do not properly account for the real world wired and wireless communication signals that suffer from signal degradation such as interference and multipath problems.
More specifically, a real world multiuser system includes a number of independent users simultaneously transmitting signals. Each of these transmissions is associated with real-time problems of multipath and co-channel interference that manifest in the received signals. Multipath occurs when a signal proceeds to the receiver along not one but many paths so that the receiver encounters signals having different and randomly varying delays and amplitudes. Co-channel interference refers to signals received from other users.
A multiuser detection (MUD) receiver can be used to jointly demodulate co-channel interfering digital signals. MUD generally refers to the detection of data in non-orthogonal multiplexes. MUD processing increases the number of information bits available per chip or signaling dimension for interference limited systems. Optimal MUD based on the maximum likelihood principle operates by comparing the received signal with the entire number of possibilities that may have occurred at the ensemble of transmitters, to give rise to the waveform received at the receiver.
However, for multiuser detectors that examine a larger capacity of signals, the computations are complex and time-consuming, thus making real-time operation impractical. Reduced complexity approaches based on conventional tree-pruning algorithms help to some extent. However, performance of such multiuser detection algorithms degrades as the parameter M (pruning factor) is decreased, but M governs the number of computations required. Thus, to combat improper pruning, basic tree-pruning must ensure that M is large enough. As a result, conventional pruning methods are still associated with increased complexity, particularly when the number of interfering signals is moderate to large.
There are a variety of methods for low complexity estimation of channel parameters in a communications system. Typically, these methods involve maximum likelihood searches (either exhaustive or directed) of the parameter space, which as used herein is the channel impulse response, and Doppler offset.
The use of such existing methods for a low complexity estimation of channel parameters, however, may involve prohibitive computational complexity for computing fully coherent or optimal solutions to parameter estimation problems based on CAF surfaces. The processing may require more time, more hardware and more sophisticated software systems. Thus, there exists a need for a low complexity method for estimation of channel parameters in a communications system.